Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?

Correct answer: 16

Solution

The bells toll together every \(\text{LCM}(2,4,6,8,10,12)=120\) seconds. In 30 minutes, i.e. 1800 seconds, they coincide at times 0, 120, 240, ..., 1800. That gives \(1800/120+1=16\) times.

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